U.S. Pat. Nos. 6,645,333 and 6,676,785, which are hereby incorporated by reference as though set forth in full, relate to methods and apparatuses for forming an improved Z-axis fiber-reinforced composite laminate structure. FIG. 9 is a graph showing the results of a shear test conducted on a 5.658 in.2, 1.0-inch-thick Z-axis fiber-reinforced composite laminate structure made by a process described in the above patents. The Z-axis fiber-reinforced composite laminate structure was pultruded and included 16 Z-axis fiber bundles per square inch deposited through the skins and core in lateral rows. The laminate was wetted out, then cured in a pultrusion die, as taught by the referenced patents. The sample was tested to ASTM C273 for shear testing (“Standard Test Method for Shear Properties of Sandwich Core Materials”). The details of this sample are as follows:
Overall thickness, 1.0 inch
Core thickness, 0.7 inch
Skin thickness, top/bottom, 0.15 inch each
Core material: Polyisocyanurate foam at 2 lb./cu. ft.
Z-axis fiber bundle density of 16 per square inch
Resin: Vinyl ester resin
Length=2.921 inches
Area=5.658 in.2 
Width=1.937 inches
From ASTM C273, the shear modulus, Gc, can be calculated from FIG. 9 as
  G  =            St      Lb        .  
From test data we see shear modulus=
                    1100        0.04            ⁢              (        0.7        )                    2.921      ×      1.937        =      3    ,    402    ⁢                  ⁢    psi  
The curve in FIG. 9 shows that at a load of 1100 lbs., the unfixed skin moves 0.040 inches. Because the area of the sample was 5.658 in.2 and there was a Z-axis fiber bundle density of 16 per square inch, there were 90.5 (5.658×16=90.5) Z-axis fiber bundles in the sample. Therefore, each Z-axis fiber bundle withstood 12.15 (1100/90.5=12.15) lbs. of load as it deflected 0.040 inches.
FIG. 10 is a simplified cross-sectional view of a Z-axis fiber bundle 110 in a composite laminate structure sample 108 in shear. The Z-axis fiber bundle 110 extends through a core 112 and is “fixed” near its ends 120 in skins 130. The body of the fiber bundle 110 takes a deflected configuration. The dashed line of FIG. 110 shows the slope of the deflection of the Z-axis fiber bundle 110. Using the equation for bending of a cantilevered cylinder, we get the following:
                              Δ          ⁢                                          ⁢                      (            deflection            )                          =                              PL            3                                3            ⁢            EI                                              (                  Equation          ⁢                                          ⁢          1                )            
The above load would apply to ½ of the length of the Z-axis fiber bundle 110 (0.35 inches) and ½ the deflection.
Using this method for estimating shear modulus, Equation 1 results in a deflection of 0.02 inches.
      Δ    ⁡          (      deflection      )        =                              12.15                      lb            .                          ⁢                              (                          .35              ⁢                                                          ⁢                              in                .                                      )                    3                            3        ⁢                  (                      3.0            ×                          10              6                        ⁢                                                  ⁢            psi                    )                ⁢                  (                      2.89            ×                          10                              -                6                                      ⁢                                                  ⁢                          in              ⁢                              .                4                                              )                      =          0.02      ⁢                          ⁢              inches        .                                  ⁢                                                            Note                ⁢                                  :                                                                                    P                =                                  12.15                  ⁢                                                                          ⁢                                      lb                    .                                                                                                                                                                                              L                =                                  .35                  ⁢                                                                          ⁢                  inches                                                                                                                                                                            E                =                                  Modulus                  ⁢                                                                          ⁢                  of                  ⁢                                                                          ⁢                  Elasticity                  ⁢                                                                          ⁢                  of                  ⁢                                                                          ⁢                  cured                  ⁢                                                                          ⁢                  Z                  ⁢                                      -                                    ⁢                  axis                  ⁢                                                                          ⁢                  fiber                  ⁢                                                                          ⁢                  bundle                                                                                                                                                                            I                =                                  Moment                  ⁢                                                                          ⁢                  of                  ⁢                                                                          ⁢                  Inertia                  ⁢                                                                          ⁢                  of                  ⁢                                                                          ⁢                  0.088                  ⁢                                                                          ⁢                  in                  ⁢                                                                          ⁢                  diameter                  ⁢                                                                          ⁢                                      bundle                    .                                                                                          
Because the deflection value of 0.02 inches is only for ½ of the deflection, the total deflection for the Z-axis fiber bundle 110 is twice this amount, or 0.04 inches. Thus, actual shear test data indicating a total deflection of 0.04 inches correlates with the theoretical shear calculation indicating a total deflection of 0.04 inches.
This shear modulus value for the tested Z-axis fiber-reinforced composite laminate structure is low because the core 112 is made of a low density foam with a shear modulus below 300 psi (i.e., the foam is not resisting shear); only the Z-axis fiber bundles 110 resist shear. Although the tested Z-axis fiber-reinforced composite laminate structure is very good in toughness and overall density as a panel, there are a number of applications requiring greater shear resistance than that provided in this Z-axis fiber-reinforced composite laminate structure. For example, in bending applications, the Z-axis fiber-reinforced composite laminate structure should have both high flexural strength and high shear strength. Thus, a need exists to increase the shear strength of Z-axis fiber-reinforced composite laminate structures, especially in the core.
The need to increase shear strength in the Z-axis fiber-reinforced composite laminate structure increases for larger sandwich thickness applications requiring flexural stiffness and shear stiffness. When thicker Z-axis fiber-reinforced composite laminate structures are made with the process described in U.S. Pat. Nos. 6,645,333 and 6,676,785, the Z-axis fiber bundles 110 will necessarily be longer. Therefore, the length (L-term) of the Z-axis fiber bundles in equation 1 becomes greater, and because deflection is directly proportional to the cube of the length, the deflection becomes greater. Also, the shear modulus decreases as the sandwich thickness increases, making the shear deflections excessive and the fiber composite structure inadequate for larger sandwich thickness applications requiring flexural stiffness and shear stiffness.